Question
The equation y = negative StartFraction 1 Over 20 EndFraction x + 10 represents the gallons of gasoline that remain in Michelle’s car after she drives x miles. Which graph represents this equation?
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (40, 8).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 11) and (80, 8).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 12) and (125, 6).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (150, 0).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (40, 8).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 11) and (80, 8).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 12) and (125, 6).
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (150, 0).
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which graph represents the equation \( y = -\frac{1}{20}x + 10 \), let's break down the equation:
- The y-intercept is \( 10 \), which means when \( x = 0 \) (when no miles have been driven), the gasoline remaining in the car is \( 10 \) gallons.
- The slope of the line is \( -\frac{1}{20} \), which means for every \( 20 \) miles driven, \( 1 \) gallon of gasoline is used.
Now, we can analyze the options given:
1. **First option**: Line goes through points \( (0, 10) \) and \( (40, 8) \):
- From \( (0, 10) \) to \( (40, 8) \), the line decreases by \( 2 \) gallons when \( x \) increases from \( 0 \) to \( 40 \) miles.
- This means \( 40 \) miles corresponds to \( 2 \) gallons used. This checks out because \( \frac{40 \text{ miles}}{20} = 2 \) gallons, which aligns with the slope and \( y \)-intercept of the equation.
2. **Second option**: Line goes through points \( (0, 11) \) and \( (80, 8) \):
- The line does not start at \( 10 \). It starts at \( 11 \) gallons, which is incorrect.
3. **Third option**: Line goes through points \( (0, 12) \) and \( (125, 6) \):
- This also does not start at \( 10 \) gallons, but at \( 12 \), which is incorrect.
4. **Fourth option**: Line goes through points \( (0, 10) \) and \( (150, 0) \):
- This starts at \( 10 \) gallons when \( x = 0 \), but it shows \( 150 \) miles corresponding to \( 0 \) gallons. This implies that with a linear decrease, it uses \( 10 \) gallons over \( 150 \) miles. However, that yields a slope of \( -\frac{10}{150} = -\frac{1}{15} \), which does not match our equation.
From this analysis, the correct option that matches the equation \( y = -\frac{1}{20}x + 10 \) is the **first option**: A graph that goes through points \( (0, 10) \) and \( (40, 8) \).
- The y-intercept is \( 10 \), which means when \( x = 0 \) (when no miles have been driven), the gasoline remaining in the car is \( 10 \) gallons.
- The slope of the line is \( -\frac{1}{20} \), which means for every \( 20 \) miles driven, \( 1 \) gallon of gasoline is used.
Now, we can analyze the options given:
1. **First option**: Line goes through points \( (0, 10) \) and \( (40, 8) \):
- From \( (0, 10) \) to \( (40, 8) \), the line decreases by \( 2 \) gallons when \( x \) increases from \( 0 \) to \( 40 \) miles.
- This means \( 40 \) miles corresponds to \( 2 \) gallons used. This checks out because \( \frac{40 \text{ miles}}{20} = 2 \) gallons, which aligns with the slope and \( y \)-intercept of the equation.
2. **Second option**: Line goes through points \( (0, 11) \) and \( (80, 8) \):
- The line does not start at \( 10 \). It starts at \( 11 \) gallons, which is incorrect.
3. **Third option**: Line goes through points \( (0, 12) \) and \( (125, 6) \):
- This also does not start at \( 10 \) gallons, but at \( 12 \), which is incorrect.
4. **Fourth option**: Line goes through points \( (0, 10) \) and \( (150, 0) \):
- This starts at \( 10 \) gallons when \( x = 0 \), but it shows \( 150 \) miles corresponding to \( 0 \) gallons. This implies that with a linear decrease, it uses \( 10 \) gallons over \( 150 \) miles. However, that yields a slope of \( -\frac{10}{150} = -\frac{1}{15} \), which does not match our equation.
From this analysis, the correct option that matches the equation \( y = -\frac{1}{20}x + 10 \) is the **first option**: A graph that goes through points \( (0, 10) \) and \( (40, 8) \).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.